Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points

Description

In this lecture, Professor Strang reviews counting the free parameters in a variety of key matrices. He then moves on to finding saddle points from constraints and Lagrange multipliers.

Summary

Topic 1: Find \(n^2\) parameters in \(L\) and \(U\), \(Q\) and \(R\), ...
Find \((m + n - r)r\) parameters in a matrix of rank \(r\)
Topic 2: Find saddle points from constraints and Lagrange multipliers

Related section in textbook: III.2

Instructor: Prof. Gilbert Strang